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2022, Volume 30, Issue 4: 1463-1476. doi: 10.3934/era.2022077
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High dimensional Riesz space distributed-order advection-dispersion equations with ADI scheme in compression format

  • Department of Mathematics, University of Macau, Avenida da Universidade, Taipa, Macau, China

  • Academic Editor: Xian-Ming Gu
  • Received: 30 December 2021 Revised: 15 February 2022 Accepted: 13 March 2022 Published: 23 March 2022

  • A second order alternating direction implicit scheme for time-dependent Riesz space distributed-order advection-dispersion equations is applied to higher dimensions with the Tensor-Train decomposition technique. The solutions are solved in compressed format, the Tensor-Train format, and the errors accumulated due to compressions are analyzed to ensure convergence. Problems with low-rank data are tested, the results illustrated a steeper growth in the ranks of the numerical solutions than that in related works.

    Citation: Lot-Kei Chou, Siu-Long Lei. High dimensional Riesz space distributed-order advection-dispersion equations with ADI scheme in compression format[J]. Electronic Research Archive, 2022, 30(4): 1463-1476. doi: 10.3934/era.2022077

    Related Papers:

  • A second order alternating direction implicit scheme for time-dependent Riesz space distributed-order advection-dispersion equations is applied to higher dimensions with the Tensor-Train decomposition technique. The solutions are solved in compressed format, the Tensor-Train format, and the errors accumulated due to compressions are analyzed to ensure convergence. Problems with low-rank data are tested, the results illustrated a steeper growth in the ranks of the numerical solutions than that in related works.


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